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*Indirect reasoning*1

DescriptionResearcher Amy Martino posed two related tasks to the students that highlighted the difference between additive and multiplicative reasoning. First, she asked the students: If we call the orange...

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DescriptionDuring this clip, the students discuss a task that had been posed by Erik: If I call the blue rod one, what rod will I call one half? A lively discussion centering on the definition of one half...

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Date Created1993

DescriptionThe students work on the task: If the orange rod is called fifty, what number name would I give the white rod? Sarah and Beth offer an answer immediately, and are questioned by researcher Amy Martino...

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Date Created1993

DescriptionResearcher Amy Martino asked the students to assign a number name to the white rod when the orange rod was called ten. After discussing the problem with their partners, the students joined in a whole...

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DescriptionAmy Martino leads a whole class discussion during which they talk about ways of writing number sentences for two problems: 1) How many one sixths are in one? and 2) How many one twelfths are in one?...

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DescriptionResearcher Amy Martino posed two related tasks to the students. In this clip, the students work on designing a rod that can be called one half when the blue rod is called one. Erik and Alan discuss...

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DescriptionResearcher Carolyn Maher leads a whole class discussion after the students' exploration of the problem: Which is larger, one fourth or one ninth, and by how much? Several students described their...

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DescriptionIn the third clip David, Meredith, Erik, and Alan worked to build models on the floor using rods. David built a model to test his conjecture, while Erik continued working on the thirty-six centimeter...

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Date Created1993

DescriptionIn this clip, researcher Amy Martino leads a class discussion that centers on the task: If I call the orange rod one, what number name would I give two whites? Some students suggest the number name...

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DescriptionIn the fourth clip Michael and Brian worked together to compare one half and three fourths.
Michael built a model of an orange and red train, two dark green rods, and four light green rods. He then...